A method and a device are known from German Patent Application No. DE 10 2004 018 962 for controlling the operation of a parallel shifting transmission, wherein a hydraulic circuit contains a first and a second hydraulically actuatable clutch whose clutch pressure is regulated by means of respective pressure regulating valves, and wherein a safe state of the hydraulic circuit is supposed to be guaranteed by means of a safety circuit if a fault occurs. The safety circuit is designed so that if a partial fault occurs which is associated with only one of the two clutches, that clutch is disengaged, and so that if a total fault occurs, which is associated with both clutches, the clutch whose clutch pressure is lower when the total fault occurs is disengaged, and the other clutch, whose clutch pressure is greater when the total fault occurs, is not disengaged, in order to maintain the transmission of torque through that clutch. The result is that when a partial fault occurs that is associated with only one of the two clutches, the subtransmission associated with the other clutch can be operated like an automated shift gearbox, in which the gear step intervals of the parallel shift transmission are however very coarse. On the other hand, if a total fault occurs which is associated with both clutches, it is no longer possible to shift, but rather it is possible to drive in the gear that is engaged at the moment in the parallel shift transmission, until there is an opportunity to stop.